Spatial central configurations in the five-body problem

Algebra Seminar
Monday, October 10, 2011 - 16:05
1 hour (actually 50 minutes)
Skiles 006
Universität des Saarlandes
In celestial mechanics a configuration of n point masses is called central if it collapses by scaling to the center of mass when released with initial velocities equal to zero. We strengthen a generic finiteness result due to Moeckel by showing that the number of spatial central configurations in the Newtonian five-body problem with positive masses is finite, except for some explicitly given special choices of mass values. The proof will be computational using tropical geometry, Gr√∂bner bases and sum-of-squares decompositions.This is joint work with Marshall Hampton.